A goal for any linking or equating of two or more tests is that the linking function be invariant to the population used in conducting the linking or equating. Violations of population invariance in linking and equating jeopardize the fairness and validity of test scores, and pose particular problems for test-based accountability programs that require schools, districts, and states to report annual progress on academic indicators disaggregated by demographic group membership. This instructional module provides a comprehensive overview of population invariance in linking and equating and the relevant methodology developed for evaluating violations of invariance. A numeric example is used to illustrate the comparative properties of available methods, and important considerations for evaluating population invariance in linking and equating are presented.